Probability question

Question

You are given three pennies. You will shake them in your hands and deposit them onto a table repeating the process 6 times in a row. Heads is a value of 2. Tails is a value of 3. The possible outcomes are: HHH=6, HHT=7, THH=7, HTH=7, TTH=8, HTT=8, THT=8, TTT=9. After tossing the coins as described, 6 times in a row, you get the following sequence: 7,7,7,7,7,9. What is the probability that on the very next 6 tosses of the coins you get the exact same sequence 7,7,7,7,7,9?

Answer 1

Each of those outcomes you described is equally likely (1/8). So for each shake, the probability of a 6 is 1/8, the probability of a 7 is 3/8, the probability of an 8 is 3/8, and the probability of a 9 is 1/8.

Therefore, the probability of 7,7,7,7,7,9 is equal to (3/8)(3/8)(3/8)(3/8)(3/8)(1/8) = 243/262144